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hoa [83]
3 years ago
9

Exercise 24-1 Payback period computation; uneven cash flows LO P1 Beyer Company is considering the purchase of an asset for $180

,000. It is expected to produce the following net cash flows. The cash flows occur evenly within each year. Year 1 Year 2 Year 3 Year 4 Year 5 Total Net cash flows $ 60,000 $ 40,000 $ 70,000 $ 125,000 $ 35,000 $ 330,000 Compute the payback period for this investment. (Cumulative net cash outflows must be entered with a minus sign. Round your Payback Period answer to 2 decimal place.)
Business
1 answer:
Tresset [83]3 years ago
4 0

Answer:

3.08 years

Explanation:

The computation of payback period is shown below:-

Payback period = Year up to which cumulative cash flow are negative + (Cumulative cash flow in period in A  ÷ cash flow of immediately year succeeding the period in A )

Year    Cash flow      cumulative cash flow

0          ($180,000)        ($180,000)

1            $60,000          ($120,000)

                            ($180,000 - $60,000)

2           $40,000           ($80,000)

                           ($120,000 - $40,000)

3           $70,000           ($10,000)

                           ($80,000 - $70,000)

4          $125,000           $115,000

(it will be end here because it excess from here)

Now we will put it into formula

Pay back period = 3 + (10,000 ÷ 125,000)

= 3 + 0.08

= 3.08 years

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Bond J has a coupon of 7.6%  

Bond K has a coupon of 11.6%

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first we must determine the current market price of both bonds using the yield to maturity formula:

YTM = {C + [(FV - PV) / n]} /  [(FV + PV) / 2]

  • YTM = 8.2%
  • C = coupon payment = $76 and $116
  • FV = face value or value at maturity = $1,000
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current market value of Bond J:

0.082 = {76 + [(1,000 - PV) / 12]} /  [(1,000 + PV) / 2]

[(1,000 + PV) / 2]  x 0.082 = 76 + [(1,000 - PV) / 12]

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41 + 0.041PV = 116 + 83.33 - 0.083PV

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a. If interest rates suddenly rise by 2.2 percent, what is the percentage price change of these bonds?

YTM = {C + [(FV - PV) / n]} /  [(FV + PV) / 2]

  • YTM = 8.2% + 2.2% = 10.4%
  • C = coupon payment = $76 and $116
  • FV = face value or value at maturity = $1,000
  • PV = present value or current market value = ???
  • n = 12 years

market value of Bond J:

0.102 = {76 + [(1,000 - PV) / 12]} /  [(1,000 + PV) / 2]

[(1,000 + PV) / 2]  x 0.102 = 76 + [(1,000 - PV) / 12]

102 + 0.051PV = 76 + 83.33 - 0.083PV

0.134PV = 157.33

PV = 57.33 / 0.134 = $427.84

market value of Bond K:

102 + 0.051PV = 116 + 83.33 - 0.083PV

0.134PV = 97.33

PV = 97.33 / 0.134 = $726.34

Bond J's market price will decrease by ($427.84 - $954.27) / $954.27 = -55.17%

Bond K's market price will decrease by ($726.34 - $1,276.85) / $1,276.85 = -43.11%

b. If interest rates suddenly fall by 2.2 percent, what is the percentage price change of these bonds?

YTM = {C + [(FV - PV) / n]} /  [(FV + PV) / 2]

  • YTM = 6%
  • C = coupon payment = $76 and $116
  • FV = face value or value at maturity = $1,000
  • PV = present value or current market value = ???
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current market value of Bond J:

0.06 = {76 + [(1,000 - PV) / 12]} /  [(1,000 + PV) / 2]

[(1,000 + PV) / 2]  x 0.06 = 76 + [(1,000 - PV) / 12]

30 + 0.030PV = 76 + 83.33 - 0.083PV

0.113PV = 129.33

PV = 129.33 / 0.113 = $1,144.51

current market value of Bond K:

30 + 0.030PV = 116 + 83.33 - 0.083PV

0.113PV = 169.33

PV = 169.33 / 0.113 = $1,498.50

Bond J's market price will increase by ($1,144.51 - $954.27) / $954.27 = 19.94%

Bond K's market price will increase by ($1,498.50 - $1,276.85) / $1,276.85 = 17.36%

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